arvs212 wrote:

If n and t are positive integers, is n a factor of t?

1) n= 3^n-2

2) t=3^n

pllz give reasonings...or if discussed earlier do post the link..

The answer here really depends on how S1 is written. There's a question in GMATFocus where Statement 1 reads \(n = 3^{n-2}\). Then, from S1 you can determine by inspection that n = 3, but we have no information about t, so this is not sufficient. Statement 2 is not sufficient either; n could be 3 and the answer is 'yes', or n could be 2 and the answer is 'no'. Using both together, the question 'is n a factor of t' becomes 'is 3^(n-2) a factor of 3^n', to which the answer is clearly yes, since n-2 is less than n (when you divide 3^n by 3^(n-2), you get 3^2 = 9). So the answer is C.

If, on the other hand, Statement 1 is written as in the original post above, so that the '-2' is not part of the exponent: \(n = 3^n - 2\), then from S1 you can see by inspection that n = 1. Since 1 is a factor of every positive integer, Statement 1 would then be sufficient, and the answer would be A.

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